Summary: Journal of Automated Reasoning manuscript No.
(will be inserted by the editor)
Proving Termination by Dependency Pairs
and Inductive Theorem Proving
Carsten Fuhs · J¨urgen Giesl ·
Michael Parting · Peter Schneider-Kamp ·
Stephan Swiderski
the date of receipt and acceptance should be inserted later
Abstract Current techniques and tools for automated termination analysis of term
rewrite systems (TRSs) are already very powerful. However, they fail for algorithms
whose termination is essentially due to an inductive argument. Therefore, we show
how to couple the dependency pair method for termination of TRSs with inductive
theorem proving. As confirmed by the implementation of our new approach in the tool
AProVE, now TRS termination techniques are also successful on this important class
of algorithms.
1 Introduction
There are many powerful techniques and tools to prove termination of TRSs auto-
matically. Moreover, tools from term rewriting are also very successful in termination
analysis of real programming languages like, e.g., Haskell, Java, and Prolog [18,32,37].
To measure their performance, there is an annual international Termination Competi-